# In a two child family, if one child is a boy, what is the probability that the other child is a girl? If the first child is a boy, what is the probability that the second is a girl?

Oct 15, 2015

These are two quite different questions.

#### Explanation:

(2) The first is a boy.
Then the chance of the second being a girl is $\frac{1}{2}$

(1) One of them is a boy (but we don't know which one).
With two children there are 4 a priori possibilities (in order):
BB-BG-GB-GG, each with an equal chance of $\frac{1}{4}$

The GG must be left out, because we know that one child is a boy.

There are two chances with a girl (BG and GB) out of a total of three leftover possibilities, so the chances are $\frac{2}{3}$